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Simplifying -16t2 + 84t + 5 = 0 Reorder the terms: 5 + 84t + -16t2 = 0 Solving 5 + 84t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + -5.25t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -5.25t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -5.25t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -5.25t + t2 = 0 + 0.3125 -5.25t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -5.25t + t2 = 0.3125 The t term is -5.25t. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25t + 6.890625 + t2 = 0.3125 + 6.890625 Reorder the terms: 6.890625 + -5.25t + t2 = 0.3125 + 6.890625 Combine like terms: 0.3125 + 6.890625 = 7.203125 6.890625 + -5.25t + t2 = 7.203125 Factor a perfect square on the left side: (t + -2.625)(t + -2.625) = 7.203125 Calculate the square root of the right side: 2.683863819 Break this problem into two subproblems by setting (t + -2.625) equal to 2.683863819 and -2.683863819.Subproblem 1
t + -2.625 = 2.683863819 Simplifying t + -2.625 = 2.683863819 Reorder the terms: -2.625 + t = 2.683863819 Solving -2.625 + t = 2.683863819 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + t = 2.683863819 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + t = 2.683863819 + 2.625 t = 2.683863819 + 2.625 Combine like terms: 2.683863819 + 2.625 = 5.308863819 t = 5.308863819 Simplifying t = 5.308863819Subproblem 2
t + -2.625 = -2.683863819 Simplifying t + -2.625 = -2.683863819 Reorder the terms: -2.625 + t = -2.683863819 Solving -2.625 + t = -2.683863819 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + t = -2.683863819 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + t = -2.683863819 + 2.625 t = -2.683863819 + 2.625 Combine like terms: -2.683863819 + 2.625 = -0.058863819 t = -0.058863819 Simplifying t = -0.058863819Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.308863819, -0.058863819}
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